We propose a
digital-analog quantum simulation of fermion-fermion scattering in
the context of quantum field theories (QFTs) with superconducting
circuits [1]. This quantum technology provides strong coupling
between superconducting qubits with a microwave resonator, and a
continuum of bosonic modes, which in turn allows us to implement a
discrete set of fermionic modes interacting with the bosonic
continuum. This effort may represent a significant advance towards
full-fledged quantum simulation of QFTs in a controllable system.